Pointed Hopf algebras: a guided tour to the liftings

Iván Angiono; Agustín García Iglesias

doi:10.15446/recolma.v53nsupl.83958

Publicado

2019-12-11

Pointed Hopf algebras: a guided tour to the liftings

Álgebras de Hopf punteadas: una excursión a los levantamientos

DOI:

https://doi.org/10.15446/recolma.v53nsupl.83958

Palabras clave:

Hopf algebras, Liftings, Cleft objetcs (en)
Álgebras de Hopf, Levantamientos, Objetos hendidos (es)

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Autores/as

Iván Angiono Universidad Nacional de Córdoba
Agustín García Iglesias Universidad Nacional de Córdoba

Resumen (en)
Resumen (es)

This article serves a two-fold purpose. On the one hand, it is a
survey about the classification of finite-dimensional pointed Hopf algebras with abelian coradical, whose final step is the computation of the liftings or deformations of graded Hopf algebras. On the other, we present a step-by-step guide to carry out the strategy developed to construct the liftings. As an example, we conclude the work with the classification of pointed Hopf algebras of Cartan type B₂.

Este artículo tiene un doble propósito. Por un lado, repasamos la clasificación de las álgebras de Hopf punteadas de dimensión finita con corradical abeliano, cuyo paso final es el cálculo de los levantamientos o deformaciones de álgebras de Hopf graduadas. Por otro, presentamos una guía paso a paso para llevar a cabo la estrategia desarrollada para construir los levantamientos. Concluimos el trabajo con un ejemplo donde damos la clasificación de las álgebras de Hopf punteadas de tipo Cartan B₂.

Referencias

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Cómo citar

APA

Angiono, I. y García Iglesias, A. (2019). Pointed Hopf algebras: a guided tour to the liftings. Revista Colombiana de Matemáticas, 53(supl), 1–44. https://doi.org/10.15446/recolma.v53nsupl.83958

ACM

[1]

Angiono, I. y García Iglesias, A. 2019. Pointed Hopf algebras: a guided tour to the liftings. Revista Colombiana de Matemáticas. 53, supl (dic. 2019), 1–44. DOI:https://doi.org/10.15446/recolma.v53nsupl.83958.

ACS

(1)

Angiono, I.; García Iglesias, A. Pointed Hopf algebras: a guided tour to the liftings. rev.colomb.mat 2019, 53, 1-44.

ABNT

ANGIONO, I.; GARCÍA IGLESIAS, A. Pointed Hopf algebras: a guided tour to the liftings. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. supl, p. 1–44, 2019. DOI: 10.15446/recolma.v53nsupl.83958. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/83958. Acesso em: 16 abr. 2024.

Chicago

Angiono, Iván, y Agustín García Iglesias. 2019. «Pointed Hopf algebras: a guided tour to the liftings». Revista Colombiana De Matemáticas 53 (supl):1-44. https://doi.org/10.15446/recolma.v53nsupl.83958.

Harvard

Angiono, I. y García Iglesias, A. (2019) «Pointed Hopf algebras: a guided tour to the liftings», Revista Colombiana de Matemáticas, 53(supl), pp. 1–44. doi: 10.15446/recolma.v53nsupl.83958.

IEEE

[1]

I. Angiono y A. García Iglesias, «Pointed Hopf algebras: a guided tour to the liftings», rev.colomb.mat, vol. 53, n.º supl, pp. 1–44, dic. 2019.

MLA

Angiono, I., y A. García Iglesias. «Pointed Hopf algebras: a guided tour to the liftings». Revista Colombiana de Matemáticas, vol. 53, n.º supl, diciembre de 2019, pp. 1-44, doi:10.15446/recolma.v53nsupl.83958.

Turabian

Angiono, Iván, y Agustín García Iglesias. «Pointed Hopf algebras: a guided tour to the liftings». Revista Colombiana de Matemáticas 53, no. supl (diciembre 11, 2019): 1–44. Accedido abril 16, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/83958.

Vancouver

1.

Angiono I, García Iglesias A. Pointed Hopf algebras: a guided tour to the liftings. rev.colomb.mat [Internet]. 11 de diciembre de 2019 [citado 16 de abril de 2024];53(supl):1-44. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/83958

Descargar cita

CrossRef Cited-by

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1. Iván Angiono, Guillermo Sanmarco. (2020). Pointed Hopf algebras over non abelian groups with decomposable braidings, I. Journal of Algebra, 549, p.78. https://doi.org/10.1016/j.jalgebra.2019.11.040.

2. Yuri Bahturin, Susan Montgomery. (2021). Group gradings and actions of pointed Hopf algebras. Journal of Algebra and Its Applications, 20(01), p.2140011. https://doi.org/10.1142/S0219498821400119.

3. Yuri Bahturin, Sarah Witherspoon. (2023). Delta Sets and Polynomial Identities in Pointed Hopf Algebras. Algebras and Representation Theory, 26(1), p.97. https://doi.org/10.1007/s10468-021-10086-2.

4. István Heckenberger, Kevin Wolf. (2021). Two-cocycles and cleft extensions in left braided categories. Journal of Algebra and Its Applications, 20(01), p.2140013. https://doi.org/10.1142/S0219498821400132.